function [C, sigma] = dataset3Params(X, y, Xval, yval)
%DATASET3PARAMS returns your choice of C and sigma for Part 3 of the exercise
%where you select the optimal (C, sigma) learning parameters to use for SVM
%with RBF kernel
%   [C, sigma] = DATASET3PARAMS(X, y, Xval, yval) returns your choice of C and 
%   sigma. You should complete this function to return the optimal C and 
%   sigma based on a cross-validation set.
%

% You need to return the following variables correctly.
C = 1;
sigma = 0.3;

% ====================== YOUR CODE HERE ======================
% Instructions: Fill in this function to return the optimal C and sigma
%               learning parameters found using the cross validation set.
%               You can use svmPredict to predict the labels on the cross
%               validation set. For example, 
%                   predictions = svmPredict(model, Xval);
%               will return the predictions on the cross validation set.
%
%  Note: You can compute the prediction error using 
%        mean(double(predictions ~= yval))
%
C_try=[0.01; 0.03; 0.1; 0.3; 1; 3; 10; 30];  
sigma_try=[0.01; 0.03; 0.1; 0.3; 1; 3; 10; 30];  
  
for i=1:length(C_try)  
    C=C_try(i);  
    for j=1:length(sigma_try)  
        sigma=sigma_try(j);  
        model= svmTrain(X, y, C, @(x1, x2) gaussianKernel(x1, x2, sigma));   
        predictions = svmPredict(model,Xval);  
  
        error(j) = mean(double(predictions ~= yval));  
  
% Accumulating error from i=1:m  
        if (j==1)  
            error_j=error(j);  
        else  
            error_j=[error_j; error(j)];  
        end  
    end  
    if (i==1)  
        error_i=error_j;  
    else  
        error_i=[error_i error_j];  
    end              
      
end  
  
% Display the error_i in matrix  
error_i  
  
% Locate the index of the minimum value in matrix error_i  
[r,c]=find(error_i==min(min(error_i)));  
  
% Optimum C and sigma are identified from the matrix above  
C=C_try(c);  
sigma=sigma_try(r);  
  
% Optimum value of C and sigma are:  
%C=1;  
%sigma=0.1;  





% =========================================================================

end
